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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Physical Law from Polynomial Truncation on the Product Flag Manifold Fl₁,₂(ℂ³) × ℂP¹

Authors: Kirk, Harold D.;

Physical Law from Polynomial Truncation on the Product Flag Manifold Fl₁,₂(ℂ³) × ℂP¹

Abstract

This note clarifies the physical interpretation of the product flag manifoldM = Fl₁,₂(ℂ³) × ℂP¹ within a unified geometric framework for fundamental physics. The manifold is not a background or configuration space, but the structured space of unrealized possibility. Physical process is identified with the irreversible contraction of accessible Kähler volume Ω, governed locally by the bridge lawd/dτ lnΩ = −πΓ(τ). Different physical regimes arise as successive Kähler quotients of M, forming a nested hierarchy of effective manifolds. Each quotient inherits the same geometric structures (volume form, curvature, and contraction dynamics), but with reduced dimensionality and accessible volume. The central result is that physical laws emerge as geometric scars of polynomial truncation of the Kähler potential under contraction. At each depth, only a characteristic polynomial degree survives: • Quartic (degree 4): particle physics and Higgs/gauge self-interactions• Quadratic (degree 2): relativity and metric structure• Linear (degree 1): classical mechanics• Constant (degree 0): black hole limit This establishes a structural origin for the form of physical laws across scales: dynamics at each regime are uniquely constrained by the surviving curvature invariants of the underlying geometry. Measurement is interpreted as a projection between contraction depths: an observer, defined by its own polynomial degree, can only resolve structure of equal or lower order. This provides a unified geometric account of quantum measurement, classical determinism, and horizon phenomena. The framework recasts physics as a single contraction hierarchy on a uniquely selected compact Kähler manifold, where time, scale, and law all emerge from the progressive reduction of possibility.

Keywords

time generation, geometric physics, CP¹, quantum measurement, product flag manifold, flag manifold, bridge law, Kähler geometry, spacetime emergence, contraction of possibility, emergence, polynomial truncation, Higgs potential, regime formation

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
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